# Customers arrive at a ferry ticket office at the rate of 14 per hour on Monday morn-

## Question:

Customers arrive at a ferry ticket office at the rate of 14 per hour on Monday morn- ings. This can be described by a Poisson distribution. Selling the tickets and pro- viding general information takes an average of 3 minutes per customer and varies exponentially. One ticket agent is on duty on Mondays.

**a.** What is the average length of the line on Monday mornings?

**b.** On average, how long does a customer wait to buy a ticket on Monday mornings (in minutes)?

**c.** How long does it take to successfully buy a ticket on Monday mornings (in min- utes)? (This includes time waiting in line and purchasing from the agent.)

**d.** What is the probability that an arriving customer has to wait to buy a ferry ticket on Monday morning?

**e.** What is the probability of exactly four customers in the ferry ticket office? This includes both customers waiting in line and those being served.

## Step by Step Answer:

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